Monomialization of Morphisms from 3-Folds to Surfaces / / by Steven D. Cutkosky

• Autore: Cutkosky Steven D
• Pubblicazione: Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2002
• Edizione: 1st ed. 2002.
• Descrizione fisica: 1 online resource (VIII, 240 p.)
• Disciplina: 516.35
• Soggetto topico: Geometry, Algebraic; Algebraic Geometry
• Classificazione: 14D06; 14E15
• Note generali: Bibliographic Level Mode of Issuance: Monograph
• Nota di contenuto: 1. Introduction -- 2. Local Monomialization -- 3. Monomialization of Morphisms in Low Dimensions -- 4. An Overview of the Proof of Monomialization of Morphisms from 3 Folds to Surfaces -- 5. Notations -- 6. The Invariant v -- 7. The Invariant v under Quadratic Transforms -- 8. Permissible Monoidal Transforms Centered at Curves -- 9. Power Series in 2 Variables -- 10. Ar(X) -- 11.Reduction of v in a Special Case -- 12. Reduction of v in a Second Special Case -- 13. Resolution 1 -- 14. Resolution 2 -- 15. Resolution 3 -- 16. Resolution 4 -- 17. Proof of the main Theorem -- 18. Monomialization -- 19. Toroidalization -- 20. Glossary of Notations and definitions -- References.
• Sommario/riassunto: A morphism of algebraic varieties (over a field characteristic 0) is monomial if it can locally be represented in e'tale neighborhoods by a pure monomial mappings. The book gives proof that a dominant morphism from a nonsingular 3-fold X to a surface S can be monomialized by performing sequences of blowups of nonsingular subvarieties of X and S. The construction is very explicit and uses techniques from resolution of singularities. A research monograph in algebraic geometry, it addresses researchers and graduate students.
• Titolo autorizzato: Monomialization of morphisms from 3-folds to surfaces
• ISBN: 3-540-48030-7
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910144941903321
• Lo trovi qui: Univ. Federico II
• Serie: Lecture Notes in Mathematics, . 0075-8434 ; ; 1786